By the rise and rapid growth of E-Commerce, use of credit cards for online purchases has more increased and it caused an explosion in the credit card fraud. The most accepted payment mode is credit card for both online as well as regular purchase, pay bills etc. So frauds associated with it are also rising. In real life, fraudulent transactions are scattered with genuine transactions and simple pattern matching techniques are not often sufficient to detect those frauds accurately. Implementation of efficient fraud detection systems has thus become imperative for all credit card issuing banks to minimize their losses. Many modern mechanisms are developed such as CHIP & PIN the mechanism do not prevent the most common fraud type such as fraudulent credit card usages over virtual POS terminals through internet or mail orders. Finally fraud detection is the essential for stop such type of frauds. In this study, classification model based on Artificial Neural Networks (ANN) and Logistic Regression (LR) are developed and applied on credit card fraud detection problem.